How Far is the 4th Maximum from the Central Maximum?

[5hassay]

Homework Statement

How far would the fourth maximum be from the central maximum, provided the distance between maxima is $$6. \times 10^{-3} m$$ and this is double-slit light interference?

Homework Equations

See solution.

The Attempt at a Solution

It is known that the central maximum in double-slit light interference is the central bright band on the screen.
Using the notation mth maximum (not mth-order maximum), the central maximum would be the first maximum (m=1) and the fourth maximum (m=4) would be the third maximum away.
It is known that the distance between adjacent nodal lines (minima -- destructive interference) is defined as,
$$\Delta x = \frac{\lambda L}{d}$$
This is equal to the distance between adjacent maxima.
So, because there is three equal spaces between adjacent nodal lines from the central maximum to the fourth maximum (using mth maximum notation):
$$x_{m} = (m - 1) \Delta x$$
, where, x_m is the distance from the mth maximum to the centre, and m is the mth maximum.

Therefore:
$$x_{4} = (4 - 1) \times 6. \ast 10^{-3} m$$
$$x_{4} = 2. \ast 10^{-2} m$$

I feel like there is some terminology in there this in incorrect, even though I am using what two texts state. Maybe I am getting confused, but I would greatly appreciate to know if I did this correctly with the correct statements and terminology. Similarly, if I did not, I would equally appreciate knowing what I am doing wrong.

Thanks! :)

 

[kuruman]

The central maximum is at x = 0 (origin). If the separation between maxima is λL/d, then the distance between the origin and the 1st maximum will be

x₁=1*(λL/d)

The distance between the origin and the 2nd maximum will be

x₂=2*(λL/d)

The distance between the origin and the 3rd maximum will be

x₃=3*(λL/d)

So ...

 

[5hassay]

The central maximum is at x = 0 (origin). If the separation between maxima is λL/d, then the distance between the origin and the 1st maximum will be

x₁=1*(λL/d)

The distance between the origin and the 2nd maximum will be

x₂=2*(λL/d)

The distance between the origin and the 3rd maximum will be

x₃=3*(λL/d)

So ...

Okay, I think my confusion is cleared up now. I do believe I understand.

Thank you very much for your time and help!